Artist Jaume Plensa brings majestic installations to the Venice Art Biennale

Take Vaporetto Number 2 from St Mark's Square to the island of San Giorgio Maggiore and, five minutes later, mass tourism has vanished. The largely empty island is dominated by Andrea Palladio's 16th-century church – a sublime but simple combination of two pediments, dome and a later bell-tower. Inside, for Venice's Biennale, you will find Together – new works by Jaume Plensa, the Barcelona sculptor best-known for "perforated" sculpture: enormous heads of stainless steel mesh that allow you to look inside and outside the human body.

For San Giorgio Maggiore, Plensa has constructed one of these great heads, just inside Palladio's entrance. A little girl stares down the nave to another Plensa sculpture – a hand hanging in mid-air, its fingers twisted in the traditional sign of benediction, used by statues all over the church. Reflecting Plensa's love of texts, the stainless steel hand is made of perforated letters from Latin, Hebrew, Arabic, Chinese, Greek, Japanese, Cyrillic, and Hindi.

It's reminiscent of the piece, Breathing, that Plensa made for BBC Broadcasting House in 2008, in memory of journalists killed while upholding freedom of speech. The sculpture – also constructed of perforated letters – is a cone on top of the building that fires a jet of light 1,000 metres into the air to mark the beginning of the BBC's 10 O'Clock News.

San Giorgio Maggiore is a unique combination of religion, art and Palladian architecture.

It has been a Benedictine monastery since AD 982. Today, the senior abbot and a fellow monk are admiring the hand in benediction. They like how it chimes with the Christian concept of the word made flesh.

The monastery has been an artistic hotbed since 1949, when Count Vittorio Cini founded the Giorgio Cini Foundation on the island in memory of his son, killed in an aeroplane accident. The count renovated the monastery, set up a library and turned San Giorgio Maggiore into a venue for concerts and art shows. At a time when the number of monks and priests is in freefall across Italy, San Giorgio Maggiore is a model of how to inject life into the country's religion.

The show was set up by the Benedicti Claustra Onlus, the not-for-profit foundation run by the order of monks at the Basilica, and Plensa had several talks with the monks of San Giorgio Maggiore before embarking on his work. "I was entering their world and I wanted to be sure I was in perfect dialogue with the basilica," he says.

Plensa isn't intimidated by working, literally, in Palladio's shadow. "I don't think too much about him," Plensa says. "The scale is key – but scale is not a problem of size. It's to do with an attitude to place, an intuition. I don't look at Palladio and me as different histories – we are both part of history. He would have had to consider similar things when he built it. He wasn't building a villa; he was building for a specific religion. In any case, my work never masks architecture."

It's true – you can see Palladio's symmetrical lines clearly through the metal whorls of Plensa's vast head, modelled on a girl he knows in Barcelona. And the blessing hand casts a lettered shadow on the church walls as the strong Venetian lunchtime light strikes the windows. The effect of Plensa's work was particularly striking in his two vast heads in the Yorkshire Sculpture Park in 2011: the green hills and dales of Yorkshire were transformed by the prism of the sculptures. "You could see the landscape through the heads," he says, "And at the same time, the landscape becomes part of the heads. My work is often about how we are from the inside," he says.

Not all Plensa's works have that perforated quality. In a hall next to the church he has placed five girls' heads in a row, lit by spotlights. With the smooth alabaster finish, their elongated dimensions and their closed eyes, they emit a shimmering, hologram-like serenity.

"The eyes are closed to give a feeling of interior thought, of the quality of a dream," he says. "A reminder of the beauty inside ourselves."

In Venice, where there is so much external beauty to admire, San Giorgio Maggiore provides rare breathing space to examine the internal variety.

When and where

Jaume Plensa, Together, 7 May-22 November, San Giorgio Maggiore, Venice